In a pushdown automaton P=(Q,Σ,Γ,δ,q0,F), a transition of the form, where…

In a pushdown automaton P=(Q,Σ,Γ,δ,q0,F), a transition of the form,

where $p,q \in Q$$a \in \Sigma \cup \{ \epsilon \}$, and $X,Y \in \Gamma \cup \{ \epsilon \}$ represents

$(q,Y) \in \delta(p,a,X).$

Consider the following pushdown automaton over the input alphabet $\Sigma = \{a,b\}$ and stack alphabet $\Gamma = \{ \#, A\}$. 

The number of strings of length 100 accepted by the above pushdown automaton is ___________ .